AQA A-Level Physics Paper 2, June 2025: Question 9

1 mark · Medium difficulty · Multiple Choice

Determine how the temperature of a constant mass of gas varies with pressure using a pressure-volume graph.

Practise this question

Question

Question 09 shows a graph of pressure in kilopascals against volume in cubic centimetres for a constant mass of gas. The pressure axis ranges from 0 to 180 kPa in intervals of 20 kPa, and the volume axis ranges from 0 to 1800 cm³ in intervals of 200 cm³. The curve is a smooth inverse curve passing through (100, 160), (200, 80), (400, 40), (800, 20), and (1600, 10). The question asks how the temperature of the gas behaves as pressure increases, with multiple-choice options: A decreases as pressure increases, B increases as pressure increases, C is constant as pressure increases, D is a maximum when pressure is 40 kPa.

Mark scheme

Show the mark scheme Mark scheme for question 9 showing the correct option is C: 'is constant as the pressure increases', with assessment objective AO2 and 1 mark.

How to answer it

Thermal Physics: Analysing a Pressure–Volume Curve

📋 What this question tests

This question assesses your understanding of the ideal gas equation ( pV = nRT ), Boyle’s Law, and your ability to quantitatively interrogate graphical data rather than relying on qualitative assumptions. You need to identify whether a curve represents an isothermal change by testing coordinate pairs along the line.

Question 09

Temperature Variation Along a p–V Gas Curve

Multiple Choice • 1 Mark (AO2)

✅ Correct Answer

C: is constant as the pressure increases.

Mark Scheme: Option C (AO2) — 1 mark

The curve is a rectangular hyperbola where the product p × V is constant at every single point. Because pV = nRT and the mass of gas is constant, temperature T must remain constant throughout.

💡 Key Knowledge

  • Ideal Gas Equation: pV = nRT = NkT .
  • Boyle’s Law: For a fixed mass of gas at constant temperature, pressure is inversely proportional to volume:
    p ∝ 1 / V ⟹ pV = constant .
  • Isothermal Line: A hyperbolic curve on a p–V graph represents an isotherm (constant temperature).
  • Proportionality: For a fixed quantity of gas ( n is constant), temperature is directly proportional to the product of pressure and volume:
    T ∝ pV .

📐 Step-by-Step Data Verification

Never guess whether a curve is isothermal purely by its visual shape. Pick convenient coordinate points directly off the grid lines to calculate the product p × V :

  1. Point 1: At V = 100 cm³ , p = 160 kPa
    pV = 160 kPa × 100 cm³ = 16 000 kPa cm³ = 16 J
  2. Point 2: At V = 200 cm³ , p = 80 kPa
    pV = 80 kPa × 200 cm³ = 16 000 kPa cm³ = 16 J
  3. Point 3: At V = 400 cm³ , p = 40 kPa
    pV = 40 kPa × 400 cm³ = 16 000 kPa cm³ = 16 J
  4. Point 4: At V = 800 cm³ , p = 20 kPa
    pV = 20 kPa × 800 cm³ = 16 000 kPa cm³ = 16 J
  5. Point 5: At V = 1600 cm³ , p = 10 kPa
    pV = 10 kPa × 1600 cm³ = 16 000 kPa cm³ = 16 J

Conclusion: Since pV is strictly constant across the entire curve, and T = pV / (nR) , the absolute temperature T does not change.

🧠 Exam Technique

  • Spot the Isotherm: A smooth decreasing curve on a p–V diagram that approaches both axes asymptotically is often an isotherm. Verify it immediately with 2 or 3 coordinate multiplications.
  • Read the axis units: Even though converting units isn't strictly necessary to see if pV is constant, notice that kPa × cm³ = (10³ Pa) × (10⁻⁶ m³) = 10⁻³ J . Checking constancy requires only the raw product.
  • Eliminate distractors: If pV is constant, T cannot increase, decrease, or have a local maximum. This immediately eliminates A, B, and D.

❌ Common Errors & Examiner Traps

  • Confusing Adiabatic and Isothermal curves: An adiabatic curve is steeper ( pVγ = constant , where γ > 1 ). In an adiabatic compression, temperature rises. Students who confuse the two choose B.
  • Intuitive misconception ("Pressure causes heating"): Thinking that compressing a gas automatically raises its temperature. In real slow compressions with heat exchange, the process is isothermal.
  • Misreading Option D: Looking at p = 40 kPa (which sits near the "bend" of the curve) and guessing that something special or maximum occurs there. Mathematical curves of the form y = k/x have no maximum or minimum value.

Topics

Physics · 3.6 Further mechanics and thermal physics (A-level only)

Question and mark scheme from the AQA A-Level Physics examination, Paper 2, June 2025. QuestionVault is an independent revision resource; questions remain the copyright of the awarding body.